Estimation of finite mixture models of skew-symmetric circular distributions

Miyata, Yoichi; Shiohama, Takayuki; Abe, Toshihiro

doi:10.1007/s00184-019-00756-z

Cited by 8 publications

(3 citation statements)

References 20 publications

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“…Recently, Miyata et al (2019) have discussed the ordinary identifiability of a finite mixture of SSWC distributions when the true number of components is known. However, Less is known about the generic identifiability of finite mixture of asymmetric circular distributions.…”

Section: Discussionmentioning

confidence: 99%

Identifiability of asymmetric circular and cylindrical distributions

Miyata¹,

Shiohama²,

Abe³

2019

Preprint

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A new method to prove the identifiability of asymmetric circular and cylindrical distributions, which utilizes Teicher's approach, is proposed.We use the simultaneous Diophantine approximations and the trigonometric moments of circular random variables to check some conditions of the proposed method. We prove the identifiability of a general sine-skewed circular distribution including the sine-skewed von Mises and sine-skewed wrapped Cauchy distributions, and a cylindrical distribution combining the sine-skewed von Mises distribution on the circle and the Weibull distribution on the non-negative linear under suitable parameter spaces.

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Section: Discussionmentioning

confidence: 99%

Identifiability of asymmetric circular and cylindrical distributions

Miyata¹,

Shiohama²,

Abe³

2019

Preprint

Self Cite

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“…More generally, Holzmann et al (2004) established conditions for the identifiability of mixtures of location-scale extensions of wrapped circular models including the wrapped symmetric α-stable, wrapped normal, and WC distributions. Mixtures with circular triangular (McVinish and Mengersen 2008), skew-rotationally symmetric (Miyata et al 2020), and power Batschelet (Mulder et al 2020b) components have also been considered.…”

Section: Circular Modelsmentioning

confidence: 99%

Recent advances in directional statistics

Pewsey

García‐Portugués

2021

TEST

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Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere, and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper, we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (Wiley 1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, space situational awareness, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. AnWe are most grateful to three anonymous referees and, in alphabetical order, to

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“…More generally, Holzmann et al (2004) established conditions for the identifiability of mixtures of location-scale extensions of wrapped circular models including the wrapped symmetric α-stable, WN, and WC distributions. Mixtures with circular triangular (McVinish and Mengersen, 2008), skew-rotationally-symmetric (Miyata et al, 2019), and power Batschelet (Mulder et al, 2020) components have also been considered.…”

Section: Circular Modelsmentioning

confidence: 99%

Recent advances in directional statistics

Pewsey¹,

García‐Portugués²

2020

Preprint

View full text Add to dashboard Cite

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial, and spatio-temporal data. We end with an overview of presently available software for analyzing directional data.

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Estimation of finite mixture models of skew-symmetric circular distributions

Cited by 8 publications

References 20 publications

Identifiability of asymmetric circular and cylindrical distributions

Identifiability of asymmetric circular and cylindrical distributions

Recent advances in directional statistics

Recent advances in directional statistics

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